First of all, it was good that Barack Obama and his people did not permit applause or reaction of any sort until the very end of his speech on the intervention in Libya on Monday night before a military audience in Washington. A high school pep rally for a war, even a small war, is a distasteful thing. At least we've learned that from the last decade.

What else have we learned? To cut to the chase, according to the president, we learned to keep our goals more modest than regime change. This was, for me, the most powerful and direct part of tonight's speech: where he said openly and plainly that the goal of this exercise was not to oust Muammar Gaddafi. "To be blunt," he said, "we went down that road in Iraq." It took eight years and cost 5,000 American lives – and many tens of thousands more Iraqi lives. Regime change isn't our job.

But this could be a hard sell, in no small part because of the way both his political foes and the media tend to simplify things: if Gaddafi is still in there, Mr President, doesn't that mean you've failed?

Barack Obama made, for my money, a credible case as to why that wasn't so. This was a humanitarian effort designed to prevent a slaughter and weaken Gaddafi to the point that the rebels have a fair shot at excising the guy. But that is their job, not the US's, or the UN's, or the Nato-led coalition's: "They will be able to determine their own destiny, and that's as it should be."

Pundits won't go for this, by and large. Pundits want to see a winner and a loser. Only then are things clear. Also, pundits want something they can call an "Obama Doctrine". But that wasn't here, on Monday night. The doctrine was: yes, we should, when we can … but it depends. And though punditry won't like it, that's the right posture.

As for the American public, it's a new concept for people to wrap their heads around. Is a limited mission something people can understand? Is it something they'll accept? It's a little bit like having as one's ultimate goal getting to kiss your girlfriend by the third date. It's human nature to have something more ambitious in mind.

I think a majority of Americans will go with it – provided this doesn't get messy and complicated. The rebels are gaining. Let's say that, in the near term, they capture a Gaddafi stronghold or two, and the dictator's battlements are so degraded by coalition bombing that some of his people see the writing on the wall and desert him. That doesn't seem implausible to me. If it goes something like that, Libya goes down in history with Grenada and Panama. Nice little war. Nice little speech.

But if we hit 90 days and Gaddafi is still holding on, and those $100m a day are starting to add up to something meaningful – and in the meantime, we've had a government shutdown, driving home how broke we are – then the war and this speech may be looked at rather differently.

Obama, of course, hopes for the former scenario, and in this sense, the speech was very Obama. He appealed to his countrypersons' better angels, believing that they should and would care that thousands of Libyans (wherever Libya is) were about to be butchered. (This, I thought, was not very strongly presented and could have been made much more alarming.) He is counting on them to respond in kind, bah, to what the cable yakkers say.

They will, but only if time demonstrates that this has worked. That, in turn, reflects more generally where Obama stands right now with the public. There is still good will, from a majority, but it is an impatient good will, and one that demands positive results without much delay. As his day of facing the voters again draws nearer, you can bet he and his people are profoundly aware of this.

The "points for trying" era is over – in Libya and on the economy. Humanitarianism is all right. Provided it works.